# Math Counterexamples

- Published in 2014
- Added on
2018-05-09

In the collection

I initiated this website because for years I have been passionated about Mathematics as a hobby and also by “strange objects”. Mathematical counterexamples combine both topics. The first counterexample I was exposed with is the one of an unbounded positive continuous function with a convergent integral. I took time to find such a counterexample… but that was a positive experience to raise my interest in counterexamples. According to Wikipedia a counterexample is an exception to a proposed general rule or law. And in mathematics, it is (by a slight abuse) also sometimes used for examples illustrating the necessity of the full hypothesis of a theorem, by considering a case where a part of the hypothesis is not verified, and where one can show that the conclusion does not hold. By extension, I call a counterexample any example whose role is not that of illustrating a true theorem. For instance, a polynomial as an example of a continuous function is not a counterexample, but a polynomial as an example of a function that fails to be bounded or of a function that fails to be periodic is a counterexample. While I’m particularly interested in Topology and Analysis, I will also try to cover Logic and Algebra counterexamples.

## Links

## Other information

- key
- MathCounterexamples
- type
- online
- date_added
- 2018-05-09
- date_published
- 2014-06-10

### BibTeX entry

@online{MathCounterexamples, key = {MathCounterexamples}, type = {online}, title = {Math Counterexamples}, author = {Jean-Pierre Merx}, abstract = {I initiated this website because for years I have been passionated about Mathematics as a hobby and also by “strange objects”. Mathematical counterexamples combine both topics. The first counterexample I was exposed with is the one of an unbounded positive continuous function with a convergent integral. I took time to find such a counterexample… but that was a positive experience to raise my interest in counterexamples. According to Wikipedia a counterexample is an exception to a proposed general rule or law. And in mathematics, it is (by a slight abuse) also sometimes used for examples illustrating the necessity of the full hypothesis of a theorem, by considering a case where a part of the hypothesis is not verified, and where one can show that the conclusion does not hold. By extension, I call a counterexample any example whose role is not that of illustrating a true theorem. For instance, a polynomial as an example of a continuous function is not a counterexample, but a polynomial as an example of a function that fails to be bounded or of a function that fails to be periodic is a counterexample. While I’m particularly interested in Topology and Analysis, I will also try to cover Logic and Algebra counterexamples.}, comment = {}, date_added = {2018-05-09}, date_published = {2014-06-10}, urls = {http://www.mathcounterexamples.net/}, collections = {Lists and catalogues}, url = {http://www.mathcounterexamples.net/}, year = 2014, urldate = {2018-05-09} }